Unveiling hidden energy poverty using the energy equity gap

Income-based energy poverty metrics ignore people’s behavior patterns, particularly reducing energy consumption to limit financial stress. We investigate energy-limiting behavior in low-income households using a residential electricity consumption dataset. We first determine the outdoor temperature at which households start using cooling systems, the inflection temperature. Our relative energy poverty metric, the energy equity gap, is defined as the difference in the inflection temperatures between low and high-income groups. In our study region, we estimate the energy equity gap to be between 4.7–7.5 °F (2.6–4.2 °C). Within a sample of 4577 households, we found 86 energy-poor and 214 energy-insecure households. In contrast, the income-based energy poverty metric, energy burden (10% threshold), identified 141 households as energy-insecure. Only three households overlap between our energy equity gap and the income-based measure. Thus, the energy equity gap reveals a hidden but complementary aspect of energy poverty and insecurity.

2nd tier is energy poverty. Only three households overlap between EEG 2nd tier (energy poor) and those with an energy burden greater than 10%.
Supplementary Figure 9. A comparison of R2 values of household temperature response functions using two models: the quadratic temperature response function used to calculate inflection temperatures in this paper (see Equation 1 in the main text), and a 5-point piecewise linear function that calculates a separate heating and cooling inflection points. N = 4104 for both models. Each box and whiskers plot indicates the minima and maxima of r-squared values of each model (the lower and upper bound of the whiskers), the first and third quantiles (the lower and upper bound of the box), and the median (the middle line). The outliers are shown as dots on either side of the whiskers. Source data can be found in our code repository.

Supplementary Tables
Supplementary Table 1   Supplemental Information Note 2: Lower income groups have older homes The variability in residence age across income groups is displayed in Supplementary Figure 3.
Here we find that lower income groups tend to have older residences, with the median house age greater than thirty years old. While the higher income group tends to reside in newer homes, with the highest income groups residing in homes with a median age of less than 20 years.

Supplemental Information Note 3: Black population experiences the most inequity in energy usage
Supplementary Figure 4 shows the breakdown of median inflection temperatures by ethnicities by year. We see large inequalities within the black population from the wide vertical spread of the median inflection temperatures. The lowest income group in the black population may be receiving aid, lowering their inflection temperature below income group 2. We also see the lowest income group in the Hispanic population is even more worse off compared to the other ethnicities. We do not see a discernable difference in temperature preference across ethnicities, so ethnicity is not statistically a good indicator of inflection temperature. We want to note that the limited data for Black and Asian populations may contribute to uncertainty.
Supplemental Information Note 4: Age could indicate temperature preference, need to distinguish between preference for warm temperatures and energy limiting behavior Supplementary Figure 5 compares the energy equity gap across age groups. There are statistically significant differences between median inflection temperatures across age groups (see table   3 in the main text), indicating that there is little chance that these variations occur solely due to chance.
For the youngest group, the energy equity gap increased sharply (>14°F) between years 3 and 4, while for the older populations, the energy equity gap had little change in comparison. From an energy poverty targeting standpoint, this highlights that within the elderly population, all residents should be targeted to reduce inflection temperatures, while for the youngest age groups, the most effective poverty eradication policy would be to target low-income groups.
For all age groups except for the oldest, the later increase in the energy equity gap is from lowincome households getting worse off and high-income households performing better, most evident in groups 18-24 and 25-34. The difference in inflection temperatures between age groups may be attributed to each age group's different temperature comfort levels. Elders may prefer warmer indoor temperatures, and cooling air from an AC system may inflame arthritis, but we should be very cautious when differentiating between a comfortably warm temperature and one that puts the resident at risk for a heat-related illness 1 .

Supplemental Information Note 5: Energy equity gap analysis for a subset of data
We present an analysis of the energy equity gap across a subset of households in Supplementary Supplemental Information Note 7: How many households can the energy equity gap capture in addition to those with high energy burden?
Supplementary Figure 8 shows a proportionate Venn diagram of households in each of the energy equity gap zone (low risk, energy insecure, and energy poor), and households with an energy burden over 10%. The corresponding data can be found in Table 2 of the main text.

Supplemental Information Note 8: Regression between inflection temperatures, housing characteristics and demographics
To understand the relationship between household level inflection temperatures and housing characteristics, as well as the relationship between income and housing characteristics and demographics, in our secondary regression, we first regressed household inflection temperatures against income groups and other variables (type of residence [i.e., single-family home, multi-family home, condo, mobile home, townhouse], residence age, residence size, number of AC units, ethnicity, and age). We find that income is correlated with all five variables (Supplementary Table 2). Thus, because these variables are not independent of each other, including income, the type of residence, residence age, residence size, number of AC units, ethnicity, and age in one analysis will introduce multicollinearity into the model, which interfere could influence our estimate of the relationship between income and inflection temperatures.
To further confirm this finding, we use the variance inflation factor (VIF). Supplementary Table 1 displays the regression output with inflection temperature as the dependent variable, and type of residence, residence age, residence size as the independent variables, along with variance inflation factor for each independent variable. The variance inflation factor provides an indication of whether an independent variable is correlated with another variable in the same regression model. When the variance inflation factor has a value of 1, the variable is not correlated with any other variable. The higher the variance inflation factor, the higher the chance of introducing multicollinearity into the model when both variables are included. We see that the residence size and income dummy variables have variance inflation factors close to or larger than 5, meaning including them in the same model would be double counting their effects on the dependent variable, the inflection temperature. From these findings, we conclude that using income as the only dependent variable to be compared to the inflection temperature is appropriate. Nonetheless, despite the collinearity issue, Supplementary Table 1 shows that the highest income groups have the lowest inflection temperatures (as reflected by the negative coefficients), which is consistent with our main conclusion.

Supplemental Information Note 9: Preferences versus inequities
When it comes to comfortable temperature preferences across different groups of people and cultures, the lack of thermostat data for the households in this study makes preference difficult to gauge. In addition, the data only records the demographics of one person filling out the survey, meaning it does not capture multiracial families. Our objective is to provide utility companies with a method to identify energy-limiting behavior in different demographic groups. The electricity utility company we collaborated with collected electricity consumption data at the household level, but does not have information on electricity consumption by appliance. We acknowledge that there will be varying electricity consumption preferences across different demographics, but we note that preferences are influenced by a number of factors (e.g., perceived amount of spending available, body mass index, preferred climate, etc.). In our distinctions we see a wide variation within income groups (Figures 5b and   5d) as well as most racial, ethnicity and age groups. However, when investigating the groups as a whole, we find low-income groups are as a whole waiting longer to start using AC systems in the summer (i.e.,  Additionally, within the quadratic 75% of households had a fit over 0.7. This finding of the nonlinear function producing a stronger fit is consistent with results from previous studies 13,17 .